Digital receivers typically sample the received signal, and process these samples in order to perform a variety of functions. It is important in such receivers to sample the received signal at the instants when a data element such as a symbol is present. Accordingly, receivers recover the timing at which data elements are received and use this timing to control sampling of the received signal.
Timing recovery deals with finding the ideal sample times to recover the received symbols from a received signal. Mismatch between the transmitter and receiver clocks complicates the recovery process because slight differences between these clocks causes a signal to be sampled at the wrong times, contributing to intersymbol interference.
One popular technique for recovering timing in a receiver is known as the Gardner technique. FIG. 1 illustrates a waveform representing data that might be received at a receiver. In the limited case of FIG. 1, the data is +1 −1 −1 +1. This waveform assumes that the transmitted data is confined to a binary constellation containing only values of −1 and +1, although it can be shown that the Gardner technique works as well for larger constellations. As shown by FIG. 1, the received signal is sampled at two times the data rate.
The Gardner technique essentially forms a timing error according to b(a−c). As long as the sampling is exactly synchronized with respect to the received data, the quantity b(a−c) is zero. For example, in the case of a transition from +1 to −1 as shown in FIG. 1, b is zero so that the quantity b(a−c) is zero. In the case of no transition so that two adjacent bits have the same value such as −1 and −1 as shown in FIG. 2, b is no longer zero. However, a and c have the same value so that the quantity b(a−c) is again zero.
If the sampling timing is not exactly synchronized to the received data, the quantity b(a−c) is not zero but, instead, takes on a value that is a measure of how far off the sampling is from the optimal sampling instants. This value is the timing error and may be used to re-synchronize the sampler to the received data.
Although the Gardner technique works reasonably well in the case of white Gaussian noise such as electronic thermal noise or atmospheric noise, it does not work as well in the case of multi-path reception of the transmitted signal.
The present invention relates to the accurate recovery of timing even in the presence of multi-path reception of a transmitted signal.